2. Triangles are cool!

3. What is a perpendicular bisector in a triangle? What is a median in a triangle? goes through the midpoint and is perpendicular to the side connects a vertex to the midpoint of the opposite side midpoints What do you call the intersection of the perpendicular bisectors? circumcenter What do you call the intersection of the medians in a triangle? centroid Are the circumcenter and centroid the same point?

4. An altitude in a triangle goes through a vertex and is perpendicular to the opposite side. vertex perpendicular ALTITUDE

5. The intersection of the three altitudes in a triangle is called the orthocenter. That’s a fun word!

6. Where is the orthocenter in a triangle located? A C B Classify this triangle by angles. The altitudes go through a vertex and are perpendicular to a side. Where is the orthocenter?

7. What about this triangle? A C B Classify this triangle by angles. The altitudes go through a vertex and are perpendicular to a side. Where is the orthocenter?

8. And how about this one? A C B Classify this triangle by angles. The altitudes go through a vertex and are perpendicular to a side. Where is the orthocenter? Notice that two of the sides had to be extended so that an altitude could be drawn.

9. Where is the orthocenter of an acute triangle located? Inside the triangle Where is the orthocenter of an obtuse triangle located? Outside the triangle Where is the orthocenter of a right triangle located? On the right angle vertex

10. altitude / orthocenter An altitude in a triangle goes through a vertex and is perpendicular to the opposite side. The intersection of the three altitudes of the sides of a triangle is the orthocenter of the triangle. orthocenter White Note Card: Location: acute triangle: inside obtuse triangle: outside right triangle: on right angle vertex

11. B A C E AE is an altitude. What is true about the diagram? AE  BC  BEA and  CEA are both right angles. Is E a midpoint? Could E be a midpoint?

12. A special segment is drawn in each triangle. Identify each special segment.

13. What is XW? Z Y X W

14. MD is an altitude in ΔLMN. Find the value for each variable. LN M D xx + 5 x + 1 (n² - n)° a c Find the value for a, c, n, and x. LN = 4x - 1

15. Make a Venn diagram to compare perpendicular bisectors, medians, and altitudes. Perpendicular bisectors Medians Altitudes True for all three Altitudes and  bisectors only Medians and Altitudes only  bisectors and Medians only True of medians only True of altitudes only True of  bisectors only

16. Circumcenters, centroids, orthocenters - some of the coolest words I’ve ever said!